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- W305319904 abstract "This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a domain by a random cover. In particular we obtain a general formula for the chance that a collection of finitely many compact connected random sets placed on a 1-complex $X$ has a union equal to $X$. The result is derived under certain topological assumptions on the shape of the covering sets (the cover ought to be {em good}), but no a priori requirements on their distribution. An upper bound for the coverage probability is also obtained as a consequence of the concentration inequality. Techniques rely on a formulation of the coverage criteria in terms of the Euler characteristic of the nerve complex associated to the random cover." @default.
- W305319904 created "2016-06-24" @default.
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- W305319904 date "2012-07-04" @default.
- W305319904 modified "2023-09-27" @default.
- W305319904 title "Random covers of 1-complexes and the Euler characteristic" @default.
- W305319904 hasPublicationYear "2012" @default.
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